where \(h\)  stands for Planck constant and \(n\)  is known as the non-Hermitian Chern number defined in Ref.  [1]}. We observe that this response can no longer be proportional to the Chern number of the non-Hermitian system. The response \(\sigma _H\)  for the non-Hermitian system can be divided into two terms. The first term is the Chern number of the non-Hermitian system, while the second term can be treated as a correction that suggests the relationship between the Chern number and the conductance might fail for open systems, which is not quantized and a delay in the response can be found [2]}. Specific details would be clearer after simplifying Eq. (REF ), lead to
\(\begin{aligned}\sigma _H =& {\mathrm {Re}(\sigma _H) } + i\mathrm {Im}(\sigma _H)\\=& \frac{e^{2}}{ h } [(N-Im(N_{\Gamma }))+iRe(N_{\Gamma })],\end{aligned}\) 
